15
-15
-30
30 E. None of the above
Answer is Wrong!
Answer is Right!
The correct answer is $\boxed{\text{B) }-15}$.
To convert a binary number to decimal, you can use the following steps:
- Starting from the right, multiply each digit by 2 raised to the power of its position, starting with 0 for the rightmost digit.
- Add the products together.
- If the number is negative, add 1 to the result.
In this case, the binary number is $1000000000001111$.
- The rightmost digit is 1, so we multiply it by 2 to the power of 0, which is 1.
- The next digit is 0, so we multiply it by 2 to the power of 1, which is 2.
- The next digit is 0, so we multiply it by 2 to the power of 2, which is 4.
- The next digit is 0, so we multiply it by 2 to the power of 3, which is 8.
- The next digit is 0, so we multiply it by 2 to the power of 4, which is 16.
- The next digit is 1, so we multiply it by 2 to the power of 5, which is 32.
- The next digit is 1, so we multiply it by 2 to the power of 6, which is 64.
- The next digit is 1, so we multiply it by 2 to the power of 7, which is 128.
- The next digit is 1, so we multiply it by 2 to the power of 8, which is 256.
- The next digit is 1, so we multiply it by 2 to the power of 9, which is 512.
- The next digit is 1, so we multiply it by 2 to the power of 10, which is 1024.
Adding the products together, we get $1000000000001111 = -15$.
Since the number is negative, we add 1 to the result to get $-15 + 1 = \boxed{\text{B) }-15}$.